The low score doesn't
shift the average down much because the four 10 point scores weight
the average toward nine. Here the high scores occurred 4 out of 5
times or 80% of the time. Only one out of five scores was low at 5.
The abundant high scores have more influence on the average. You can
calculate the weighted average in the following way. Literally what
happens in the calculation is

average
score = [40 points + 5 points][1/5] =
[45 points] = 9 points

Example
weighted average calculation using isotope abundances:

What is the
average atomic weight for chlorine if it has two isotopes? The percent
abundance for chlorine-35 is 75.53%. The percent abundance
for chlorine-37 is 24.4%. The mass for Cl-35 is 35.0 amu and for Cl-37
it is 37.0 amu.

Average
atomic weight = 26.4 amu + 9.05 amu = 35.5 amu

Notice
that the average is determined by the more abundant Chlorine-35.
Because chlorine-35 is more common, the average is closer to 35
amu than 37 amu. Clearly no atoms of chlorine actually have
a mass of 35.5 amu. The tabulated value in the periodic
table is a statistical creation and matches no real chlorine atoms at all.

Exercise:

What
is the average atomic mass for thallium, Tl? The two stable isotopes and their abundances are listed here.Tl-205
has a mass of 205.059 amu with an abundance of 70.48 % and Tl-203 has
a mass of 203.059 amu with an abundance of 29.52 %